Gyroscopes are currently used in a number of military and civilian applications. One common application involves using gyroscopes, known as control moment gyroscopes (CMGs) to control the attitude or orientation of a spacecraft. A CMG comprises a spinning rotor and one or more motorized gimbals, which are used to rotate the rotor (e.g., gimballing), which in turn alters the angular momentum of the rotor. This change in angular momentum produces a reactionary torque which causes the spacecraft to rotate to the desired attitude or orientation. Attitude control system and other spacecraft orienting applications generally utilize at least three CMGs, also known as a CMG array.
The direction of torque capable of being produced by an individual CMG varies as its gimbal is rotated. In addition, the maximum achievable rate of rotation of the gimbal (or gimbal rate) for the individual CMGs is limited by hardware, which in turn limits the amount of useful torque an individual CMG can produce. Commanding more torque than an individual CMG is capable of producing results in saturation of the individual CMG. Also, particular arrangements of the CMGs in the CMG array, known as singularities, limit the ability of the CMG array to produce torque in certain directions. Therefore, steering control laws or other control schemes have been developed to determine how the individual CMGs should be rotated to produce a desired overall torque (or a commanded torque), without causing singularities or saturation in the CMG array.
In some applications, it is desirable to be able to reposition a spacecraft as quickly as possible. For example, in imaging satellite applications, the satellite may need to be quickly repositioned as the satellite orbits in order to collect data for a desired target area at a desired time. As the satellite travels at a high rate of speed, for example, 14,000 miles per hour or more in orbit, the satellite must be properly positioned at a particular time during the orbit to capture data for a particular target area or region. In addition, the satellite may need to have a certain rotational velocity in order to maintain the integrity of the collected data (e.g., the images are not blurred). As a result, the spacecraft may need to be adjusted or moved with a large rotational acceleration and/or large rotational velocity. Conventional prior art attitude control systems utilize a constant torque command (or acceleration command) for the CMG array to reposition the spacecraft without saturating one or more of the CMGs. However, because the individual CMG gimbal rates vary throughout the duration of a torque command as the individual CMGs are moved, an individual CMG of the CMG array would be producing its maximum torque output at for brief instants, if at all. Thus, prior art methods fail to maximize the overall torque output capability of the CMG array.